Page 136 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 10] ROTATIONAL MOTION 121

SOLVED PROBLEM 10.19
An air compressor is powered by a 200 rad/s electric motor using a V-belt drive. The motor pulley is 8 cm
in radius, and the tension in the V-belt is 135 N on one side and 45 N on the other. Find the power of the
motor.

The torque exerted by the motor on the belt is, since the net force on the belt is the difference between the two
tensions,
τ = Fr = (135 N − 45 N)(0.08 m) = 7.2N·m

The power output of the motor is therefore
P = τω = (7.2N·m)(200 rad/s) = 1440 W = 1.44 kW

ANGULAR MOMENTUM
The equivalent of linear momentum in rotational motion is angular momentum. The angular momentum L of a
rotating body has the magnitude
L = Iω
Angular momentum = (moment of inertia)(angular velocity)

The greater the angular momentum of a spinning object, such as a top, the greater its tendency to continue to
spin.
Like linear momentum, angular momentum is a vector quantity with direction as well as magnitude. The
direction of the angular momentum of a rotating body is given by the right-hand rule (Fig. 10-5): When the
fingers of the right hand are curled in the direction of rotation, the thumb points in the direction of L.

Fig. 10-5

According to the principle of conservation of angular momentum, the total angular momentum of a
system of bodies remains constant in the absence of a net torque regardless of what happens within the
system.
Skaters performing a spin make use of conservation of angular momentum. They begin to turn with arms
and one leg outstretched and then bring them in close to the body to distribute the body’s mass nearer to the axis
of rotation, thereby decreasing the moment of inertia I. Since L must remain constant, the angular velocity ω
increases.
Because angular momentum is a vector quantity, its conservation implies that the direction of the axis of
rotation tends to remain unchanged. For this reason a spinning top stays upright, whereas a stationary one falls
over immediately.
Table 10.1 compares linear and angular quantities.